Envelope functions and asymptotic structures in Banach spaces
Tom 164 / 2004
Studia Mathematica 164 (2004), 283-306
MSC: 46B20, 46B45, 46B07.
DOI: 10.4064/sm164-3-6
Streszczenie
We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic-$\ell _p$ spaces in terms of the $\ell _p$-behavior of “disjoint-permissible” vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey–Pisier theorem.
